Non-uniform density sample analyzing method, device and system

ABSTRACT

A non-uniform density sample analyzing method for analyzing distribution state of particle-like matter in a non-uniform density sample, wherein an actually measured X-ray scattering curve is an in-plane X-ray scattering curve obtained by in-plane diffraction measurement, wherein the fitting between the in-plane X-ray scattering curve and the simulated X-ray scattering curve is performed, and wherein the value of the fitting parameter when the simulated X-ray scattering curve agrees with the in-plane X-ray scattering curve serves to indicate the in-plane direction distribution sate of the particle-like matter in the non-uniform density sample. This method can analyze the in-plane direction distribution state of the particle-like matter in the anisotropic non-uniform density sample easily and accurately. Its device and system are also disclosed.

TECHNICAL FIELD

[0001] The present invention relates to a method, device and system foranalyzing a non-uniform density sample, and more particularly to a novelnon-uniform density sample analyzing method, non-uniform density sampleanalyzing device and non-uniform density sample analyzing system capableof simply, accurately analyzing an in-plane direction distribution stateof particle-like matter in the non-uniform density sample.

BACKGROUND ART

[0002] A method for analyzing a particle diameter distribution in anon-uniform density sample such as a porous film by using an X-ray hasbeen newly proposed by the inventors of the present invention (seeJapanese Patent Application No. 2001-088656). In this method, a diffusescattering intensity of the X-ray is measured and the particle diameterdistribution is analyzed based on the measured intensity, therebyrealizing an excellent analyzing ability.

[0003] However, there is yet room for improvement in such an excellentanalyzing method so as to achieve another new advantage.

[0004] That is, with the non-uniform density sample analyzing methoddisclosed in the Japanese Patent Application No. 2001-088656, it isdifficult to completely analyze the density non-uniformity of ananisotropic non-uniform density-sample.

[0005] To be specific, a non-anisotropic non-uniform density sample is asample in which particle-like matter such as fine particle and pore hasa random distribution as shown in, for example, FIG. 1(a). Conversely,as shown in, for example, FIGS. 2(a) and 2(b), the anisotropicnon-uniform density sample is a sample in which the distribution ofparticle-like matter has some regularity or directivity in an in-planedirection. In the example of FIG. 2(b), the particle-like matter isdistributed in the in-plane direction with the regularity in whichclusters each having two pentagons connected to each other are formed.

[0006] As for the non-anisotropic non-uniform density sample, if anX-ray scattering curve is measured by scanning an X-ray outgoing angleθ_(out) with an X-ray incident angle θ_(in) being constant in acondition of, for example, θ_(in)=θ_(out)+offset Δω, the densitynon-uniformity of the sample in a direction corresponding to a directionof a scattering vector q shown in FIGS. 1(a) and 1(b), i.e., a directionnear a plane normal is measured as described in the Japanese PatentApplication No. 2001-088656. This is so-called out-of-plane diffractionmeasurement.

[0007] If this out-of-plane diffraction measurement is directly appliedto the anisotropic non-uniform density sample, the non-uniformity of thesample is measured along the scattering vector q in the direction nearthe plane normal shown in FIGS. 2(a) and 2(b) similarly to FIG. 1. Thismeans that the anisotropic non-uniform density sample cannot be analyzedin an in-plane direction of the sample. With the non-anisotropicnon-uniform density sample, by contrast, the in-plane direction of thesample is random. Therefore, even if a scan direction is changed, theparticle-like matter can be observed without any changes and thus nodisadvantage occurs. With the anisotropic non-uniform density sample,however, because of the regularity of the particles in the in-planedirection as described above, the particle-like matter is observeddifferently according to the scan direction. As a result, the particlediameter distribution in the in-plane direction cannot be analyzed withthe out-of-plane diffraction measurement.

[0008] The present invention has been achieved in light of thesesituations and it is an object of the present invention to provide anovel non-uniform density sample analyzing method as well as anon-uniform density sample analyzing device and a non-uniform densitysample analyzing system capable of simply and highly accuratelyanalyzing the distribution state of the particle-like matter in theanisotropic non-uniform density sample in the in-plane direction.

DISCLOSURE OF INVENTION

[0009] In order to achieve the foregoing, the present invention,provides a non-uniform density sample analyzing method comprising thesteps of: calculating a simulated X-ray scattering curve under the samecondition as a measurement condition of an actually measured X-rayscattering curve by using a scattering function which represents anX-ray scattering curve according to a fitting parameter which indicatesdistribution sate of particle-like matter; and carrying out fittingbetween the simulated X-ray scattering curve and the actually measuredX-ray scattering curve while changing the fitting parameter, wherein thevalue of the fitting parameter when the simulated X-ray scattering curveagrees with the actually measured X-ray scattering curve serves toindicate the distribution state of the particle-like matter in anon-uniform density sample, thereby analyzing the distribution state ofthe particle-like matter in the non-uniform density sample, wherein theactually measured X-ray scattering curve is an in-plane X-ray scatteringcurve obtained by in-plane diffraction measurement, wherein the fittingis carried out between the in-plane X-ray scattering curve and thesimulated X-ray scattering curve, and wherein the value of the fittingparameter when the simulated X-ray scattering curve agrees with thein-plane X-ray scattering curve serves to indicate the in-planedirection distribution state of the particle-like matter in thenon-uniform density sample (claim 1). The present invention alsoprovides the analyzing method, wherein the fitting parameter of thescattering function indicates the in-plane direction distribution stateof the particle-like matter (claim 2).

[0010] Further, the present invention provides a non-uniform densitysample analyzing device, comprising: function storage means for storinga scatting function which represents an X-ray scattering curve accordingto a fitting parameter which indicates distribution state ofparticle-like matter; simulation means for calculating a simulated X-rayscattering curve in the same condition as a measurement condition of anactually measured X-ray scattering curve by using the scatteringfunction stored in the function storage means; and fitting means forcarrying out fitting between the simulated X-ray scattering curve andthe actually measured X-ray scattering curve while changing the fittingparameter, and wherein the value of the fitting parameter when thesimulated X-ray scattering curve agrees with the actually measured X-rayscattering curve serves to indicate the distribution state of theparticle-like matter in a non-uniform density sample, wherein theactually measured X-ray scattering curve is an in-plane X-ray scatteringcurve obtained by in-plane diffraction measurement, wherein the fittingis carried out between the in-plane X-ray scattering curve and thesimulated X-ray scattering curve, and wherein the value of the fittingparameter when the simulated X-ray scattering curve agrees with thein-plane X-ray scattering curve serves to indicate the in-planedirection distribution state of the particle-like matter in thenon-uniform density sample (claim 3). The present invention alsoprovides the analyzing device, wherein the fitting parameter of thescattering function indicates the in-plane direction distribution stateof the particle-like matter (claim 4).

[0011] Moreover, the present invention provides a non-uniform densitysample analyzing system for analyzing distribution state ofparticle-like matter in a non-uniform density sample, comprising: anin-plane diffraction measuring device which performs in-planediffraction measurement of an actually measured X-ray scattering curvefor the non-uniform density sample; and the non-uniform density sampleanalyzing device according to claim 3 or 4.

BRIEF DESCRIPTION OF DRAWINGS

[0012] FIGS. 1(a) and 1(b) are illustrations each for explainingout-of-plane diffraction measurement conducted to a non-anisotropicnon-uniform density sample.

[0013] FIGS. 2(a) and 2(b) are illustrations each for explainingout-of-plane diffraction measurement conducted to an anisotropicnon-uniform density sample.

[0014] FIGS. 3(a), 3(b), and 3(c) are illustrations each for explainingin-plane diffraction measurement conducted to the anisotropicnon-uniform density sample.

[0015]FIG. 4 is a flow chart for explaining a non-uniform density sampleanalyzing method according to the present invention.

[0016]FIG. 5 is a block diagram for explaining a non-uniform densitysample analyzing device and a non-uniform density sample analyzingsystem according to the present invention.

[0017]FIG. 6 illustrates a particle diameter model as a shape model ofparticle-like matter.

[0018]FIG. 7 illustrates the relationship among an X-ray incident angle,a penetrating depth, and a reflectivity.

[0019]FIG. 8 illustrates a simulated X-ray scattering curve and anin-plane X-ray scattering curve as one example of the present invention.

[0020]FIG. 9 illustrates a particle distribution of particles in anin-plane direction as one example.

[0021]FIG. 10 illustrates a structural factor of the particle-particlecorrelation as one example.

[0022]FIG. 11 is a flow chart for explaining a non-uniform densitysample analyzing method described in Japanese Patent Application No.2001-088656.

[0023]FIG. 12 is a block diagram for explaining a non-uniform densitysample analyzing device and a non-uniform density sample analyzingsystem described in the Japanese Patent Application No. 2001-088656.

[0024] Reference symbols in the drawings denote the following system,device, or elements:

[0025]1 Non-uniform density sample analyzing system

[0026]2 X-ray measuring device

[0027]3 Non-uniform density sample analyzing device

[0028]31 Critical angle storage means

[0029]32 Function storage means

[0030]34 Fitting means

[0031]35, 36 Output means

[0032]301 Function storage means

[0033]302 Simulation means

[0034]303 Fitting means

[0035]304, 305 Output means

[0036]4 In-plane diffraction measuring device

BEST MODE FOR CARRYING OUT THE INVENTION

[0037] The present invention applies in-plane diffraction measurement tothe non-uniform density sample analyzing method described in theJapanese Patent Application No. 2001-088656 so as to realize analysis ofan anisotropic non-uniform density sample in an in-plane direction.

[0038] As shown in FIG. 3(c), the in-plane diffraction measurementutilizes in-plane diffraction wherein if an X-ray is incident on asurface of a sample at a very small incident angle θ_(in), then an X-raycomponent in parallel to the sample surface appears in the sample, theX-ray component is diffracted by a crystal surface perpendicular to thesample surface and diffracted in plane at a diffraction angle 2θ_(ø),and a diffraction line of the diffracted X-ray component is emitted at avery small angle θ_(out) relative to the sample surface.

[0039] According to this in-plane diffraction measurement, as shown inFIGS. 3(a) and 3(b), a scattering vector q′ in the in-plane direction ofthe non-uniform density sample can be measured. Therefore, by employingthe scattering vector q′ (hereinafter, “in-plane X-ray scatteringcurve”) as an actually measured X-ray scattering curve in thenon-uniform density analyzing method described in the Japanese PatentApplication No. 2001-088656, the distribution state of the particle-likematter in the in-plane direction can be accurately analyzed.

[0040]FIG. 4 is a flow chart for explaining the non-uniform densitysample analyzing method of the present invention using the in-planediffraction measurement As shown in FIG. 4, with the analyzing method ofthe present invention, the measurement of the X-ray scattering curve inStep s2 of the non-uniform density analyzing method described in theJapanese Patent Application No. 2001-088652 shown in FIG. 11 is made bythe in-plane diffraction measurement (Step s20). Then, the fittingbetween the measured in-plane X-ray scattering curve and a simulatedX-ray scattering curve calculated separately (Step s10) is performed(Step s30), and the value of the fitting parameter obtained when thesimulated x-ray scattering curve and the in-plane X-ray scattering curveagree with each other serves to indicate the distribution state of theparticle-like matter in the non-uniform density sample in the in-planedirection (Steps s40 and s50).

[0041] The simulated X-ray scattering curve is calculated (Step s10) byusing a scattering function that represents an X-ray scattering curveaccording to the fitting parameter that indicates the distribution stateof the particle-like matter and by arbitrarily selecting the value ofthe fitting parameter. In this case, according to the present invention,since the distribution state of the particle-like matter in the in-planedirection is to be analyzed, the fitting parameter that represents thedistribution state of the particle-like matter in the in-plane directionis used. The following Eq. 1 illustrates one example of the scatteringfunction to which the fitting parameters that represent the distributionstate of the particle-like matter in the in-plane direction areintroduced. $\begin{matrix}{{{Eq}.\quad 1}\text{:}} \\{{I(q)} = {{S(q)} \cdot {I_{0}(q)}}} \\{q = {\frac{4\quad \pi}{\lambda}\sin \quad \theta_{\varphi}}} \\{{S(q)} = \frac{1}{1 - {C\left( {{q \times D},\eta} \right)}}} \\{{C\left( {x,\eta} \right)} = {- {\frac{24\quad \eta}{\left( {1 - \eta} \right)^{4}x^{3}}\begin{bmatrix}{{\left( {1 + {2\quad \eta}} \right)^{2}\left( {{\sin \quad x} - {x\quad \cos \quad x}} \right)} -} \\{{6\quad {\eta \left( {1 + \frac{\eta}{2}} \right)}^{2}\left( {{2\quad \sin \quad x} - {x\quad \cos \quad x} - {2\frac{1 - {\cos \quad x}}{x}}} \right)} +} \\{\frac{\eta}{2}\left( {1 + \frac{\eta}{2}} \right)^{2}\left\{ {{\left( {4 - \frac{24}{x^{2}}} \right)\sin \quad x} -} \right.} \\\left. {{\left( {x - \frac{12}{x}} \right)\cos \quad x} + {24\quad \frac{1 - {\cos \quad x}}{x^{3}}}} \right\}\end{bmatrix}}}} \\{{I_{o}\left( {q,R_{o},M} \right)} = {\frac{8\quad \pi^{2}r^{2}{{\overset{\rightharpoonup}{f}(q)}}^{2}\left( {1 + \frac{4q^{2}R_{o}^{2}}{M^{2}}} \right)^{- \frac{1 + M}{2}}}{\left( {{- 3} + M} \right)\left( {{- 2} + M} \right){\left( {{- 1} + M} \right) \cdot q^{6}}} \times}} \\{\quad \begin{bmatrix}{{M^{3}\left( {1 + \frac{4\quad q^{2}R_{o}^{2}}{M^{2}}} \right)}^{- \frac{1 + M}{2}} -} \\{{{M^{3}\left( {1 - \frac{4q^{2}R_{o}^{2}}{M^{2}}} \right)}\quad {\cos \left( {\left( {{- 1} + M} \right){\tan^{- 1}\left( \frac{2{qR}_{o}}{M} \right)}} \right)}} +} \\{\left( {{- 3} + M} \right)\left( {{- 2} + M} \right){M \cdot q^{2}}{R_{o}^{2}\left( {{\cos\left( {\left( {{- 1} + M} \right){\tan^{- 1}\left( \frac{2{qR}_{o}}{M} \right)}} \right)} +} \right.}} \\{\left. \left( {1 + \frac{4q^{2}R_{o}^{2}}{M^{2}}} \right)^{- \frac{1 + M}{2}} \right) +} \\{{\left( {{- 3} + M} \right)M^{3}\frac{4\quad q^{2}R_{o}^{2}}{M^{2}}{\cos \left( {\left( {{- 1} + M} \right){\tan^{- 1}\left( \frac{2{qR}_{o}}{M} \right)}} \right)}} -} \\{2\left( {{- 1} + M} \right)M^{2}{qR}_{o}{\sin \left( {\left( {{- 1} + M} \right){\tan^{- 1}\left( \frac{2{qR}_{o}}{M} \right)}} \right)}}\end{bmatrix}}\end{matrix}$

[0042] q=|q|: Magnitude of scattering vector

[0043] q: Scattering vector

[0044] λ: X-ray wavelength

[0045] R_(o): Mean diameter parameter of particle-like matter

[0046] M: Distribution shape parameter

[0047] D: Shortest distance parameter between particle-like matters

[0048] η: Correlation order parameter of particle-like matter

[0049] The fitting parameters of the scattering function given in thisEq. 1 are the mean diameter parameter R₀ of the particle-like matter,the distribution shape parameter M, the shortest distance parameter Dbetween the particle-like matters, and the correlation order parameter ηof the particle-like matter.

[0050] Naturally, it is necessary to calculate the simulated X-rayscattering curve in the same conditions as those for the scatteringcurve. Therefore, the conditions are set equal to in-plane diffractionmeasurement conditions.

[0051] In the in-plane diffraction, there is no need to measure areflectivity curve. Due to this, Steps s1 and s3 shown in FIG. 11 areremoved from the flow chart of FIG. 4.

[0052] In Steps s30 and s40, it is determined whether the simulatedX-ray scattering curve agrees with the in-plane X-ray scattering curve.If they do not agree, then the values of the fitting parameters arechanged, the simulated X-ray scattering curve is recalculated, and it isdetermined whether the recalculated simulated X-ray scattering curveagrees with the in-plane scattering curve.

[0053] These steps are repeated while adjusting and changing the valuesof the fitting parameters until the both curves agree with each other.The values of the fitting parameters obtained when they agree are valuesthat represent the in-plane direction distribution state of theparticle-like matter in the non-uniform density sample of the analysistarget (Step s50). In case of the Eq. 1, the mean diameter R, thedistribution shape M, the shortest distance D, and the correlation orderη of the particle-like matter are analyzed in the in-plane direction.

[0054] With this non-uniform density sample analyzing method, the X-rayincident angle θ_(in) is variously changed during the in-planediffraction measurement and the penetrating depth of the X-ray in thesample is changed, whereby the in-plane direction distribution of theparticle-like matter at any depth position in the sample can beanalyzed.

[0055]FIG. 7 illustrates one example of a change in the penetratingdepth [nm] relative to the X-ray incident angle θ_(in). As can be seenfrom FIG. 7, if the X-ray is incident on an Si surface at, for example,0.10, the penetrating depth of the X-ray is only 3 nanometers. If thein-plane diffraction measurement is made in this state, the in-planedirection distribution on a very surface of the penetrating depth of 3nanometers can be analyzed. If the incident angle is set at about 0.3°,then the penetrating depth exceeds 200 nanometers and a structuralanalysis within the range of this depth can be performed. If the sampleis a thin film, the structure of the thin film often changes on asurface and an inside thereof. Therefore, the analysis of the sample inthe depth direction by variously changing the X-ray incident angle isquite effective. For example, it is possible to simply and accuratelydetermine whether the film is formed uniformly in the depth direction.

[0056]FIG. 5 is a block diagram for explaining a non-uniform densitysample analyzing device for executing the non-uniform density sampleanalyzing method described above and a non-uniform density analyzingsystem that includes the non-uniform density analyzing device. Asillustrated by FIG. 5, the analyzing system according to the presentinvention includes an in-plane diffraction measurement device (4) thatmeasures in-plane diffraction in place of an X-ray measurement device(2) in the non-uniform density analyzing system described in theJapanese Patent Application No. 2001-088656 shown in FIG. 12.

[0057] As the in-plane diffraction measurement device (4), aconventional, well-known device can be employed. For example, there isknown a device proposed by the present inventor (see Japanese PatentApplication Laid-Open No. 11-287773). The device disclosed in theJapanese Patent Application Laid-Open No. 11-287773 is constituted sothat a parabolic multilayer monochromator formed by alternatelyproviding heavy element layers and light element layers a plurality oftimes and having a surface, on which an X-ray is incident, formed as aparaboloid so as to facilitate creating a parallel X-ray beam having alarge intensity and to realize highly reliable in-plane diffractionmeasurement even at experimental level and so that a goniometer capableof scanning the X-ray not only in a direction orthogonal to the surfacebut also a direction parallel to the surface is combined with theparabolic multilayer film monochromator. By employing this device as thein-plane diffraction measuring device (4), the analyzing system of thepresent invention can realize the analysis of the particle-like matterin the in-plane direction using the in-plane X-ray scattering curve bythe highly reliable in-plane diffraction measurement without the need oflarge-scale equipment. If the device disclosed in the Japanese PatentApplication Laid-Open No. 11-287773 is applied to the present invention,the device is not specially adjusted or changed either structurally oroperationally. Therefore, reference is made to the Japanese PatentApplication Laid-Open No. 1′-287773 for the detailed description of thestructure and operation of the device.

[0058] Meanwhile, the non-uniform density sample analyzing device (3)includes a function storage means (301) which stores a scatteringfunction (e.g., Equation 1) having fitting parameters that represent thedistribution of the particles in the in-plane direction, a simulationmeans (302) which calculates a simulated X-ray scattering curve usingthe scattering function from the function storage means (301), and afitting means (303) which performs fitting between the simulated X-rayscattering curve from the simulation means (302) and the in-plane X-rayscattering curve from the in-plane diffraction measuring device (4).Until the fitting means (303) determines that the simulated X-rayscattering curve agrees with the in-plane X-ray scattering curve, thesimulation means (302) repeatedly calculates the simulated X-rayscattering curve while selecting and changing the fitting parameterusing the least square method or the like. Then, the value of thefitting parameter obtained when the both curves agree is output, as ananalysis result that represents a distribution state of theparticle-like matter in the non-uniform density sample in the in-planedirection, to output means (304) and (305) such as a display, a printer,and a storage means.

[0059] In the non-uniform density sample analyzing method of the presentinvention, calculation steps such as simulation and fitting steps areexecuted using a computer (a calculator such as a general-purposecomputer or an analysis-dedicated computer). In addition, thenon-uniform density sample analyzing device that the present inventionalso provides can be realized as, for example, software for executingfunctions of the above-stated means. Further, the non-uniform densitysample analyzing system that the present invention further provides ispreferably constituted so that data and signals can be transmitted andreceived between the in-plane diffraction measurement device and thenon-uniform density sample analyzing device in either both or onedirection.

EXAMPLE

[0060] An actual analysis result for the anisotropic non-uniform densitysample will now be explained.

[0061]FIG. 8 illustrates the simulated X-ray scattering curve obtainedby the scattering function of Equation 1 and the in-plane X-rayscattering curve obtained by the in-plane diffraction measurement. As isobvious from FIG. 8, the excellent fitting of the both curves isrealized. The fitting parameters when the both curves agree are asfollows:

[0062] Mean diameter parameter R_(o)=7.0 nm,

[0063] Distribution shape parameter M=5.0,

[0064] Shortest distance parameter D=10 nm, and

[0065] Correlation order parameter η=0.28.

[0066] These values are the mean diameter, the distribution shape, theshortest distance, and the correlation order of the particle-like matterin the anisotropic non-uniform density sample in this example. Thediameter distribution of the particle-like matter in the in-planedirection is shown in FIG. 9. And, FIG. 10 illustrates the relationshipbetween the particle diameter and the structural factor S(Q).

[0067] Needless to say, this invention is not limited to the embodimentand various modifications can be made to details of the invention.

INDUSTRIAL APPLICABILITY

[0068] As described above in detail, according to the non-uniformdensity sample analyzing method, the non-uniform density sampleanalyzing device, and the non-uniform density sample analyzing system ofthe present invention, the distribution state such as the particlediameter distribution of the particle-like matter even in theanisotropic non-uniform density sample in the in-plane direction can besimply, highly accurately analyzed.

1 A non-uniform density sample analyzing method comprising the steps of:calculating a simulated X-ray scattering curve under the same conditionas a measurement condition of an actually measured X-ray scatteringcurve by using a scattering function which represents an X-rayscattering curve according to a fitting parameter which indicatesdistribution sate of particle-like matter; and carrying out fittingbetween the simulated X-ray scattering curve and the actually measuredX-ray scattering curve while changing the fitting parameter, wherein thevalue of the fitting parameter when the simulated X-ray scattering curveagrees with the actually measured X-ray scattering curve serves toindicate the distribution state of the particle-like matter in anon-uniform density sample, thereby analyzing the distribution state ofthe particle-like matter in the non-uniform density sample, wherein theactually measured X-ray scattering curve is an in-plane X-ray scatteringcurve obtained by in-plane diffraction measurement, wherein the fittingis carried out between the in-plane X-ray scattering curve and thesimulated X-ray scattering curve, and wherein the value of the fittingparameter when the simulated X-ray scattering curve agrees with thein-plane X-ray scattering curve serves to indicate the in-planedirection distribution state of the particle-like matter in thenon-uniform density sample. 2 The non-uniform density sample analyzingmethod according to claim 1, wherein the fitting parameter of thescattering function indicates the in-plane direction distribution stateof the particle-like matter. 3 A non-uniform density sample analyzingdevice, comprising: function storage means for storing a scattingfunction which represents an X-ray scattering curve according to afitting parameter which indicates distribution state of particle-likematter; simulation means for calculating a simulated X-ray scatteringcurve in the same condition as a measurement condition of an actuallymeasured X-ray scattering curve by using the scattering function storedin the function storage means; and fitting means for carrying outfitting between the simulated X-ray scattering curve and the actuallymeasured X-ray scattering curve while changing the fitting parameter,and wherein the value of the fitting parameter when the simulated X-rayscattering curve agrees with the actually measured X-ray scatteringcurve serves to indicate the distribution state of the particle-likematter in a non-uniform density sample, wherein the actually measuredX-ray scattering curve is an in-plane X-ray scattering curve obtained byin-plane diffraction measurement, wherein the fitting is carried outbetween the in-plane X-ray scattering curve and the simulated X-rayscattering curve, and wherein the value of the fitting parameter whenthe simulated X-ray scattering curve agrees with the in-plane X-rayscattering curve serves to indicate the in-plane direction distributionstate of the particle-like matter in the non-uniform density sample. 4The non-uniform density sample analyzing device according to claim 3,wherein the fitting parameter of the scattering function indicates thein-plane direction distribution state of the particle-like matter. 5 Anon-uniform density sample analyzing system for analyzing distributionstate of particle-like matter in a non-uniform density sample,comprising: an in-plane diffraction measuring device which performsin-plane diffraction measurement of an actually measured X-rayscattering curve for the non-uniform density sample; and the non-uniformdensity sample analyzing device according to claim
 3. 6 A non-uniformdensity sample analyzing system for analyzing distribution state ofparticle-like matter in a non-uniform density sample, comprising: anin-plane diffraction measuring device which performs in-planediffraction measurement of an actually measured X-ray scattering curvefor the non-uniform density sample; and the non-uniform density sampleanalyzing device according to claim 4.